Question

All waves on the electromagnetic spectrum travel at the same speed in a vacuum. The speed of these waves in a vacuum is
3x10 m/s. As the wavelength of a wave doubles, how does the speed and frequency of the wave change?

Answer 1

Answer:

The frequency will reduced to half if you increase the wavelength to double.

The speed of the wave is constant and equal to $3\times 10^8\ m/s$.

Explanation:

The wavelength of a wave varies inversely to frequency of the wave.

The relation between the frequency and wavelength of a wave is given as:

$v=f\lambda$

Here,

$v\to \textrm{speed of the wave which is always a constant in vacuum}\\f\to \textrm{frequency of the wave}\\\lambda\to \textrm{wavelength of the wave}$

Therefore, as the wavelength increases then the frequency will decrease.

Similarly, as the wavelength of the wave decreases, then the frequency will increase.

Now, if we increase the wavelength by a factor 'k', the frequency will reduce by the same factor 'k'.

Here, the wavelength is doubled which means it increases by a factor of '2'. Therefore, the frequency will decrease by a factor of '2'.

So, the frequency will reduced to half if you increase the wavelength to double.

The speed of the wave is constant as the increase in wavelength is compensated by a decrease in frequency and thus the product of the two remains same. Therefore, speed of wave is equal to $3\times 10^8\ m/s$.